The internal circadian rhythms of cells and organisms coordinate their physiological properties to the prevailing 24-h cycle of light and dark on earth. The mechanisms generating circadian rhythms have four defining characteristics: they oscillate endogenously with period close to 24 h, entrain to external signals, suffer phase shifts by aberrant pulses of light or temperature, and compensate for changes in temperature over a range of 10°C or more. Most theoretical descriptions of circadian rhythms propose that the underlying mechanism generates a stable limit cycle oscillation (in constant darkness or dim light), because limit cycles quite naturally possess the first three defining properties of circadian rhythms. On the other hand, the period of a limit cycle oscillator is typically very sensitive to kinetic rate constants, which increase markedly with temperature. Temperature compensation is therefore not a general property of limit cycle oscillations but must be imposed by some delicate balance of temperature dependent effects. However, ''delicate balances'' are unlikely to be robust to mutations. On the other hand, if circadian rhythms arise from a mechanism that concentrates sensitivity into a few rate constants, then the ''balancing act'' is likely to be more robust and evolvable. We propose a switch-like mechanism for circadian rhythms that concentrates period sensitivity in just two parameters, by forcing the system to alternate between a stable steady state and a stable limit cycle.bistability ͉ homoclinic bifurcation ͉ mathematical model ͉ nuclear transport S ince the breakthrough discovery of the period (per) gene by Konopka and Benzer in 1971 (1), molecular biologists have identified many new circadian rhythm genes and have uncovered a complex network of interacting feedback loops which comprise the control system. In the consensus view, an endogenous daily rhythm is created by a negative feedback loop whereby the PERIOD (PER) protein inhibits its own expression by interfering with transcription factors (2, 3). This mechanism has been studied in great detail theoretically by many authors (4-12). The time-delayed negative feedback loop generates limit cycle oscillations with many properties characteristic of physiological daily rhythms, except for one: the autonomous circadian period (T) is quite insensitive to variations of the kinetic constants, a property that is not characteristic of generic limit cycle oscillators. This insensitivity shows up in two ways: (i) T varies little among individual organisms even though individuals show considerable genetic and/or proteomic variability that translates into variations of kinetic parameters, and (ii) T is temperature compensated, even though kinetic constants are strongly temperature dependent. Physiologically, this robustness of the period (T Ϸ 24 h despite genetic variability and environmental fluctuations) is essential to circadian physiology. If the autonomous period of the clock drifts too far from 24 h, then the circadian rhythm would not reliably ...

Many biological systems contain both positive and negative feedbacks. These are often classified as resonators or integrators. Resonators respond preferentially to oscillating signals of a particular frequency. Integrators, on the other hand, accumulate a response to signals. Computational neuroscientists often refer to neurons showing integrator properties as type I neurons and those showing resonator properties as type II neurons. Guantes & Poyatos have shown that type I or type II behaviour can be seen in genetic clocks. They argue that when negative feedback occurs through transcription regulation and post-translationally, genetic clocks act as integrators and resonators, respectively. Here we show that either behaviour can be seen with either design and in a wide range of genetic clocks. This highlights the importance of parameters rather than biochemical mechanism in determining the system behaviour.

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